Who is the next Steve Jobs? It’s a question that Apple shareholders will be looking at during their next meeting, where they’ll vote on a proposal to create a written policy on finding a new CEO.

In a filing released today, Apple’s board of directors opposed the proposal, arguing that it would give competitors unfair insight into Apple’s “confidential objectives and plans.” The board also said that publicly identifying CEO candidates might make those candidates a target for recruiters, while non-candidates would feel that they’d been passed over.

Since Apple is so reticent to talk about its next CEO, we’ve come up with one possible answer — Facebook chief executive Mark Zuckerberg.

Now, that probably sounds like a big stretch, but let’s look at where both companies stand. Pundits have been wondering about who will fill take Jobs’ place for a while now. They’re big shoes to fill, with the company’s success in the past decade largely attributed to Jobs’ return, particularly his product perfectionism and the “reality distortion field” he creates around the company.

This is one area where Apple may be looking worriedly at Microsoft. When founder Bill Gates stepped down, he was replaced by longtime company executive Steve Ballmer. In the decade since Ballmer took over, Microsoft stock has fallen nearly 50 percent. (Last year, Apple passed Microsoft in market capitalization.) I’m not saying that Cook or Schiller are just like Ballmer, but there’s clearly a danger in replacing a company’s visionary leader with someone who’s competent but less inspired.

Of course, it’s no secret that the big tech players have been interested in Facebook for a while now — but Apple, its profits supercharged by the iPhone, may be the one company that can still afford the deal.

What’s less certain is whether Facebook — and by Facebook, we really mean Zuckerberg — would be interested. He controls three board seats, and prizes his ability to shape the company’s direction. It’s looking increasingly likely that Facebook will hold a public stock offering in 2012.

So what would actually convince him to sell? Well, how about the chance to run the combined Apple-Facebook?

Aside from the glory of running the most valuable tech company in the world, there’s the strategic logic. The mobile and social worlds are colliding. Facebook has been trying to figure out how it can thrive in a world where platform makers like Apple and Google increasingly integrate Web services directly into devices. There have been rumors of a so-called “Facebook phone” — but with 60 million monthly users on the iPhone, isn’t Apple’s mobile device already the Facebook phone?